Abstract: We present a novel approach for dealing with optimal approximate merging of two adjacent Bézier curves with G²-continuity. Instead of moving the control points, we minimize the distance between the original curves and the merged curve by taking advantage of matrix representation of Bézier curve’s discrete structure, where the approximation error is measured by L₂-norm. We use geometric information about the curves to generate the merged curve, and the approximation error is smaller. We can obtain control points of the merged curve regardless of the degrees of the two original curves. We also discuss the merged curve with point constraints. Numerical examples are provided to demonstrate the effectiveness of our algorithms.

Key words: Approximate merging, G¹-continuity, G²-continuity, Discrete subdivision, Point constraints

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